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The magnetic constant μ 0 appears in Maxwell's equations, which describe the properties of electric and magnetic fields and electromagnetic radiation, and relate them to their sources. In particular, it appears in relationship to quantities such as permeability and magnetization density , such as the relationship that defines the magnetic H ...
The permeability of vacuum (also known as permeability of free space) is a physical constant, denoted μ 0. The SI units of μ are volt-seconds per ampere-meter, equivalently henry per meter. Typically μ would be a scalar, but for an anisotropic material, μ could be a second rank tensor. However, inside strong magnetic materials (such as iron ...
As before, it is defined by the equation ε 0 = 1/(μ 0 c 2), and is thus determined by the value of μ 0, the magnetic vacuum permeability which in turn is determined by the experimentally determined dimensionless fine-structure constant α: = = ,
The above equations are the microscopic version of Maxwell's equations, expressing the electric and the magnetic fields in terms of the (possibly atomic-level) charges and currents present. This is sometimes called the "general" form, but the macroscopic version below is equally general, the difference being one of bookkeeping.
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
In free space, where ε = ε 0 and μ = μ 0 are constant everywhere, Maxwell's equations simplify considerably once the language of differential geometry and differential forms is used. The electric and magnetic fields are now jointly described by a 2-form F in a 4-dimensional spacetime manifold.
The definitions for monopoles are of theoretical interest, although real magnetic dipoles can be described using pole strengths. There are two possible units for monopole strength, Wb (Weber) and A m (Ampere metre). Dimensional analysis shows that magnetic charges relate by q m (Wb) = μ 0 q m (Am).
μ 0 ≈ 12.566 × 10 −7 H/m is the magnetic constant, also known as the permeability of free space, ε 0 ≈ 8.854 × 10 −12 F/m is the electric constant, also known as the permittivity of free space, c is the speed of light in free space, [9] [10] The reciprocal of Z 0 is sometimes referred to as the admittance of free space and ...